Final answer:
To solve for a variable, algebraic techniques such as adding, subtracting, multiplying, or dividing are used to isolate the variable. Quadratic equations can be solved using the quadratic formula, followed by a contextual validation of the solutions.
Step-by-step explanation:
To solve for the variable, we will often need to isolate the variable on one side of the equation. This can involve various algebraic techniques such as adding, subtracting, multiplying, or dividing both sides of the equation by the same number. For example, to move a term from one side to the other, we add or subtract it from both sides. To cancel a coefficient, we multiply or divide both sides by that coefficient.
When dealing with a more complex equation like −12 = (−4x)/35, we would multiply both sides by 35 to eliminate the denominator. In the case where we have an equation such as x + 8 = 235, we would subtract 8 from both sides to isolate x. Sometimes we encounter equations with terms on both sides like 7/8 (48x−8) + 4 = 3(5x−19), where we would first distribute the multipliers inside the parentheses and then move terms to isolate the variable.
For quadratic equations, like x2 + 0.00088x − 0.000484 = 0, we can use the quadratic formula to solve for the variable's values, and then assess which solutions are valid based on the context of the problem.